2.  Charles’ Evaluation 2

3. 3 Portfolio goals – Expected annual return of at least 7.5%. – At least 50% invested in “A-Rated” investments. – At least 40% invested in immediately liquid investments. – No more than $30,000 in savings accounts and certificates of deposit. Problem summary – Determine the amount to be placed in each investment. – Minimize total overall risk. – Invest all $100,000. – Meet the investor goals (diversify).

4.  Variables X i = the amount allotted to each investment;  The Mathematical Model Minimize 25X 3 +30X 4 +20X 5 +15X 6 +65X 7 + 40X 8 ST: X 1 + X 2 + X 3 + X 4 + X 5 + X 6 + X 7 + X 8 = 100,000.04X 1 +.052X 2 +.071X 3 +.10X 4 +.082X 5 +.056X 6 +.27X 7 +.125X 8  7500 X 1 + X 2 + X 5 + X 7  50,000 X 1 + X 3 + X 4 + X 7  40,000 X 1 +X 2  30,000 All the variables are non-negative 4 Risk function Total investment Return A - Rate Liquid Savings/ Certificate

5. 5